Divided by n 3 at the same time, it is obvious that when n tends to infinity, 1/N,1/n 2,1/n 3 all tend to 0.

So it is equal to 4/5.

2. Single increase

Derivation, y' = 1/2 (e x+e (-x)), x ∈ (- 1, 2), y' >: 0.

So the function is simply added.

3.-3/2

Search by segment and remove the absolute value.

= ∫ (upper 1, lower 0)( 1-x)dx+∫ (upper 3, lower 1)(x- 1)dx

= (x- 1/2x 2) | Up 1, Down 0+( 1/2x 2-x) | Up 3, Down 1

= 1/2+2

=5/2

4. Necessary conditions. (Book Theorem)

5.3π

∫∫dxdy is the integral area.

Is a circle: 1

The area is 4π-π=3π.

That is. ∫∫dxdy =3π。

6. Infinitesimal of the same order

When x tends to 2,

(x^2-4)/(x-2)=x+2=4

So they are in the same order.

7.

Original formula = (1+2/(x- 1)) x

=

When x=3, it is a harmonic series and does not converge.

When x=-3, it is a conditionally convergent staggered series.

So the convergence domain is x ∈ [-3,3)